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A350527
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a(n) = c(n*r)*f(n/r), where f = floor, c = ceiling, and r = golden ratio (A001622).
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2
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0, 4, 5, 14, 27, 30, 48, 52, 75, 102, 108, 140, 176, 184, 225, 234, 280, 330, 341, 396, 408, 468, 532, 546, 615, 688, 704, 782, 799, 882, 969, 988, 1080, 1176, 1197, 1298, 1320, 1426, 1536, 1560, 1675, 1700, 1820, 1944, 1971, 2100, 2233, 2262, 2400, 2430
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OFFSET
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1,2
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COMMENTS
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The golden ratio r is the unique number x such that f(n*x)*c(n/x) - c(n*x)f(n/x) = n for all n >= 1.
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LINKS
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FORMULA
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a(n) = -n + A350526(n) = -n + f(n*x)*c(n/x), where f = floor, c = ceiling, and r = golden ratio.
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MATHEMATICA
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r = GoldenRatio; c[x_] := Ceiling[x]; f[x_] := Floor[x];
Table[f[n r]*c[n/r], {n, 1, 100}] (* A350526 *)
Table[c[n r]*f[n/r], {n, 1, 100}] (* A350527 *)
Table[f[n r]*c[n/r] - c[n r]*f[n/r], {n, 1, 100}] (* A000027 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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